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Sep 19, 2017 at 8:28 answer added Mateusz Kwaśnicki timeline score: 1
Sep 19, 2017 at 8:14 comment added Anthony Quas So: same example $X_n\sim \exp(\text{Unif}[0,n])$. Again, $\mathbb EX_n^2\sim e^{2n}/n$ and $(\mathbb EX_n)^2\sim e^{2n}/n^2$.
Sep 19, 2017 at 6:34 comment added gradstudent Also see the new EDIT.
Sep 19, 2017 at 6:34 history edited gradstudent CC BY-SA 3.0
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Sep 19, 2017 at 6:33 comment added gradstudent Thanks! Thats interesting! I was actually thinking of continuous distributions when I framed the question.
Sep 19, 2017 at 6:03 comment added Anthony Quas How about $X_n$ takes a uniformly chosen element of $\{2,4,8,\ldors,2^n\}$? $\mathbb E X_n^2$ is essentially $2^{2n}/n$, while $(\mathbb E X_n)^2$ is essentially $2^{2n}/n^2$.
Sep 18, 2017 at 22:07 history asked gradstudent CC BY-SA 3.0